#coding:utf8
'''
给定一个m*n的表，找到从左上到右下的最短路径的长度
这是一道很典型的动态规划问题
o  --  o  --  o
|      |      |
|      |      |
o  --  o  --  o
|      |      |
|      |      |
o  --  o  --  o

p(2,2) = min(p(2,1)+v(2,1), p(1,2)+v(1,2))
'''

class Solution(object):
    def minPathSum(self, grid):
        m = len(grid)
        n = len(grid[0])
        for i in range(1,n):
            grid[0][i] += grid[0][i-1]
        for i in range(1,m):
            grid[i][0] += grid[i-1][0]
        for i in range(1,m):
            for j in range(1,n):
                grid[i][j] += min(grid[i-1][j], grid[i][j-1])
        return grid[-1][-1]
